The generalized inverse A(2)T and its applications

  • Authors:

  • Chong-Guang Cao;Xian Zhang

  • Affiliations:

  • Department of Mathematics, Heilongjiang Univ., Harbin, P. R. China;Department of Mathematics, Heilongjiang Univ., Harbin, P. R. China and School of Mechanical and Manufacturing Engineering, The Queen's University of Belfast, Stranmillis Road, Belfast, BT9 5AH, UK

  • Venue:
  • The Korean Journal of Computational & Applied Mathematics
  • Year:
  • 2003

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Abstract

The existence and representations of some generalized inverses, including AT,*(2), AT,*(1,2), AT,*(2,3), A*,S(2), A*,S(1,2), and A*,S(2,4), are showed. As applications, the perturbation theory for the generalized inverse AT,S(2) and the perturbation bound for unique solution of the general restricted system Ax = b (dim(AT) =dimT, b ∈ AT and x ∈ T) are studied. Moreover, a characterization and representation of the generalized inverse AT,*,(2) is obtained.